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<h1 class="ltx_title ltx_title_section">Huang’s defocusing model</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">An alternative model of the defocusing curves is described by Huang
et al. <cite class="ltx_cite">[<a href="#bib.bib14" title="Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy" class="ltx_ref">1</a>]</cite>. The relationship between the axial position
of a molecule and its imaged widths along two perpendicular axes is
given by</p>
</div>
<div id="Sx1.p2" class="ltx_para">
<table id="Sx1.EGx1" class="ltx_equationgroup ltx_eqn_eqnarray">

<tr id="Sx1.Ex1" class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_td ltx_align_right"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-6px" src="mi/mi3.png" width="48" height="21" alt="\displaystyle\sigma_{1}\left(z\right)"></td>
<td class="ltx_td ltx_align_center"><img id="Sx1.Ex1.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi1.png" width="18" height="11" alt="\displaystyle="></td>
<td class="ltx_td ltx_align_left"><img id="Sx1.Ex1.m3" class="ltx_Math" style="vertical-align:-21px" src="mi/mi10.png" width="420" height="57" alt="\displaystyle\frac{w_{01}}{2}\,\sqrt{1+\left(\frac{z-c_{1}}{d_{1}}\right)+a_{1%
}\left(\frac{z-c_{1}}{d_{1}}\right)^{2}+b_{1}\left(\frac{z-c_{1}}{d_{1}}\right%
)^{4}}\,,"></td>
<td class="ltx_eqn_pad"></td>
</tr>
<tr id="Sx1.Ex2" class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_td ltx_align_right"><img id="Sx1.Ex2.m1" class="ltx_Math" style="vertical-align:-6px" src="mi/mi5.png" width="48" height="21" alt="\displaystyle\sigma_{2}\left(z\right)"></td>
<td class="ltx_td ltx_align_center"><img id="Sx1.Ex2.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi1.png" width="18" height="11" alt="\displaystyle="></td>
<td class="ltx_td ltx_align_left"><img id="Sx1.Ex2.m3" class="ltx_Math" style="vertical-align:-21px" src="mi/mi11.png" width="420" height="57" alt="\displaystyle\frac{w_{02}}{2}\,\sqrt{1+\left(\frac{z-c_{2}}{d_{2}}\right)+a_{2%
}\left(\frac{z-c_{2}}{d_{2}}\right)^{2}+b_{2}\left(\frac{z-c_{2}}{d_{2}}\right%
)^{4}}\,."></td>
<td class="ltx_eqn_pad"></td>
</tr>
</table>
<p class="ltx_p">Here <img id="Sx1.p2.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi14.png" width="128" height="19" alt="w_{01},a_{1},b_{1},c_{1},d_{1}"> and <img id="Sx1.p2.m2" class="ltx_Math" style="vertical-align:-5px" src="mi/mi15.png" width="128" height="19" alt="w_{02},a_{2},b_{2},c_{2},d_{2}">
are unknown parameters of the model which can be determined by the
calibration process.</p>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<ul id="I1" class="ltx_itemize">
<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="DefocusModels.html" title="" class="ltx_ref">Defocusing models</a></p>
</div>
</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="../estimators/ui/EllipticGaussianEstimatorUI.html" title="" class="ltx_ref">Rotated elliptical Gaussian function PSF model (3D using astigmatism)</a></p>
</div>
</li>
<li id="I1.i3" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i3.p1" class="ltx_para">
<p class="ltx_p"><a href="../estimators/ui/CalibrationEstimatorUI.html" title="" class="ltx_ref">Calibration of the imaging system</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

<ul id="L1" class="ltx_biblist">
<li id="bib.bib14" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">B. Huang, W. Wang, M. Bates and X. Zhuang</span><span class="ltx_text ltx_bib_year">(2008)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Science</span> <span class="ltx_text ltx_bib_volume">319</span> (<span class="ltx_text ltx_bib_number">5864</span>), <span class="ltx_text ltx_bib_pages"> pp. 810–3</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1126/science.1153529" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Huang’s defocusing model" class="ltx_ref"><span class="ltx_text ltx_ref_title">Huang’s defocusing model</span></a>.
</span>
</li>
</ul>
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